Data Interpretation & Logical Reasoning (DILR) Question on Problems on ages

Question

After five years, A's age will be 10.5 years less than 2.5 times of C's age. Three years ago, the ratio of age of A and C is 3: 1. If B is three times the age of C, then what is the present age of B?

Answer 1

Solution

The correct option is (C): 9:10.
Let present age of A and C are a years and c years, respectively.
(a + 5) = $\frac{5(c + 5)}{2}$ - 10.5
=> 2a + 10 = 5c + 25 - 21
=> 2a - 5c = -6 --- (1)
And $\frac{(a - 3)}{(c - 3)}$ = 3: 1
=> a - 3 = 3c - 9
=> a - 3c = -6 --- (2)
Solving (1) and (2), we get
a = 12 and c = 6
Hence, B = 3 * 6=18 years.